An inverse scattering problem with part of the fixed-energy phase shifts

Assume that q (r) is a real valued, compactly supported potential, q(r) = 0 for r := \ x \ > a, q(r) epsilon L-2(B-a), n = 3, B-a := {x : x epsilon R-n, \ x \ < a}. Let L be an arbitrary fixed subset of non-negative integers such that Sigma(l not equal 0,l epsilon L) 1/l= infinity, and {delta(l)} be fixed-energy phase shifts corresponding to q (r). The main result is: Theorem. The data {delta(l)}(For All l epsilon L), determine q(r) uniquely.